Electrical impedisivity or resistivity measuring



March 31, 1942. F, W, LEE 2,277,707

ELECTRICAL IMPEDISIVITY 0R RESISTIVITY MEASURING Filed April 8, 1938 T SH/Frm the United States Patented Mar. 31 1942 sasc'rmcsr. mrsm'srvrrv 'ou'nnslsi-v f i Y a l nvrnr Msssrmnvo 'a 'Frederick'y Lee. Owings Mills, Md. o l Reilled l'orv abandoned application "Serial No.

743.738, SeptemberlZ, 1934. This application` Aprll`8,`1938, Serial No. 200,948

12 Claims. (Cl. 175-182) (Granted under the actk or'March 3. 1883.v as f" v 811161111011 Apl'ii 30, 1928.; 370 0. G. 757) y The invention described herein may Ihe manufactured and used by or for the Government of ty thereon. l

The present case is a renie ot application Serial' f N0. 743,738, fi1ed September 12, 1934.

without payment of anyroyal-v andACz, the total current ilowing being-indicated l by current meter I. v,spaced between the current Y This invention relates to the art of electrical impedisivityz'or resistivity measuringand aims generalb' to improve the same. 'Ihev invention is particulariy'but not exclusively adapted for use .in geophysical surveying andis described hereinafter in' connection with such use;

Among the objects of the invention, severally, vare the provisionofj an improved method and means `iformeasuring electrical' resistivityzfthe* Aprovision of an improved -methodand means fior lmeasuring its alternating current "equivalent, 4herein termed impedlsivity: -and theprovision oi novel stepsand'arrangements ci partsnin` various l subcombina'tions contributing to comprehensive' aims above stated.

In the :art of geophysical surveying, it is well lknown that -by producing a currentfleld in a f medium, as the earths `crust i'or example, and

taking measurements ofcurrent and potential` at proper pointsfof the medium, datamay beobtained, from which; alter measurement of the geometrical constants ori the medium,r 'its electrical resistivity may be calculated. IAsfseti'orth in my prior Patent No. 1,951,760, grdntedMarch I 20,1934, the formulae for such( calculationsl inelectrodes C; and Ca.' and in the form shown along a straight line.r extending between them, are potential ground contacts Pi and Pz, andthe .diiIerence in ground potential-at thesel electrodes maybe indicated byfa voitm'eter E.

Y rssyshmvn Ain Figure ;-1,-1ths potential electrode P1 isl spaced tromtherespective current elec- "nate's resistivity:v '20,

trodeslfC1 and Cz,n by distances' rifand mj and f the potential velectrode-'Ps tits spaced from the current electrodesCi and (la vby the distances r:

anden, respectively. l Y* y d l `Principle` of Voperation and vgeneraly method The mathematical relations ci' current and potential in Figure ima'y thus be represented by the following equation in .vg'hicl'tgrhoqia)- desig- "1;"19 Now ii' the total distance ybetween the current Ielectrodes C1 and Czbe designated d, itis clear lying between C1 a and Pi f andV that n, rz, ra, and n.' may be expressed as percentages oi' d;Vv Using'- Kiyas the per cent of d Kr -as thepergcent ol d lying between vCr and Pi, then u volve the geometric spacings of the electrodes and the current and potential observations.

- The present invention', in its more ccmprehen sive aspects, a`s applied to geophysical surveying, greatly simplifies the procedure in makin'gfsuch surveys, enables ydirect vmeasurement of th'e'ap'- 1'1== K1 lid htt-Rnd while j y 12F-#Had and 1'4=(1.-' Ks)d l substttutmgtneseivalues in 'Equation 1 and reducing, l yieidszr.

KK n In some geophysical measurementsIiS-and-11':

parent earth resistivityA and dielectric constants oi' the'fgr'ound without elaborate j computations which' have heretofore been neeessary.` and sa'ves l frequently as much as 50%' ofthejneldmans time; as'vwellas'eliminating the possibilities 'of error incident;

u the previously requiredscorn-- putations;

In'the accompanying drawingi'form'ingfa o! the presentspeciiications, Y y v u Figure 1 isv a diagrammatic representation in perspective ot an 'arrangement ofjelectrodesxfor measuring ground resistivity,V and i Figure 2 snows dlagrammatieauy the-r method and means of this invention adapted `for use; in

the arrangement ot Figure 1.y s n In the simple l, arrangement for measurin ground resistivity shown in Figure 1, the battery B supplies current to thecurrent electrodes `C1 may not lie onfthestraight line joiningthecur- -rent Velectrodes Ci and l C.' Under these circumstances Kl `and-Iii: become complex `fractions such as=o.5 +f.4, 1n which! is the square'roct ofminum` `crie, In. such-instances it wili'bem'ore convenf ient, and will simplify, the field technique.-r to employy the system of my :copending f application Serial No. 200,947, led April '8; l1938,' entitled "Geophysical surveyin|`.;",.Iv i f However, it Ewill bessen vthatwhether Ki and Ki are real or complex for agiven configuration oi' applied electrodes, the entire bracketed portion oi' Equation 2 isa constant; and that if this ybracketed portiony be represented by K the equa'- By solvingI this' equation for resistivity *u prnzgl-nE.;

Now\the present invention contemplates preferable condition that the factor v asa be kept constant. 'rmsmaybe accomplished by (EqT 4) ioAv changing the valuevof the current I for changes y in the ground spacing d, in constant` ratio.

In addition, the present invention contemplates t as a preferred condition that thisratio voi'4 e bel made equal to K divided by 2r. This may be accomplished by proper proportioning of the scale of the current meter. l i l Under these preferred conditions it is apparent that Equation 4 will reduce to .,:E ',(Eqes) and that the voltmeter or potentiometer E may thus, by' this invention, be made to indicate directly the electricalresistivity being measured.

In embodyingthis method Vin the meter of lmy rinvention special shunts are employed, together with a means for adjusting the'current to speciiied values for dierent selected distances d. rFor simplicity the scale of d andI may be made the same or simple multiples for ,fractions'of each other. I h --l Even more flexible results maybe obtained by my invention by assigning to the fraction a definite valve, say m.` Under `these conditions I may be measured in amperes as well asin terms of d in any system of units, either current or distances,`and Equation 4 willl become:

- (Eq'. a) As exemplifying"r suitable. arrangements which may be` made to enable adjustment fof; the scale v reading' Es with reference to the,V actual voltage E the invention contemplates that multiplier re-l sistances or a current shunt, as a part of a po- Atentiometer dropl wire, may be used, as herein- 'after explained; n*

. It is, of course. understood that adjustments are iiexibl'e enough to' permit simple scalemultiples or decimals for any range of observation.

Simplified species of method` Now, applying the general method above out'- y for anl Aactualginput of 191;,miliivolts. the

yreading El will'be 100 units,1'then u and the value a to the distance n. we nnd `from Equation 1 that:

Ip 1 l l 1 Ez-r (Eq. la)

which, reduced, and solved for Vthe resistivity,

yields:

Jl' (Eq. 4a)

Now, if d is measured in feet, E in millivolts, and I in miliiamperes, and it is desired to determine "resistivity in ohm-centimeters. bearing in mind that one tootequals 30.48 centimeters, and 2f equals 8.2838, for this equi-spaced electrode arrangement; v

P (6.2838) (30.48)]2'0 K a l I whence Now, ii value of I in lmilliampersbe made equal to, or a simple multiple of, the value of a in feet, asa/.1000, then v f y y ',:Qieir (Emsa) Then if an adjustment of scale according -to the method of, this invention is made,.sothat scale -Y,=1oo sa Ilor the purpose of explaining the fundamentais of the method of this invention. reference has been had above tooperations in which a di- .rect current field vis appliedto the material in- 'be used, and that'the preferred embodiment of lined to the simple case in which rz`=2r1, and

r3=2r4 (i. e. in which the distances 011%; PiPz; PzCz are all equal and on the same straight line),

vestig'ated. Itwill be apparent, however, from the following description that this direct current discussion exemplifies the method as performed with either direct or alternating current.

Y mussrou simpues'cirme e e vReferring now to the illustrative simpliiied circuit shown in Figure 2, it will be seen that either direct current-oralternsting current ymay the inventionemhodies electrical circuits Vadapted i'or the use o'f either.

'I'hus,` the current circuit or i I, form shown; consists .of a source'of power, herein shown as eitherv a battery Il or alternating current source Il, which may be connected in the circuit by a suitable switch |45, herein a doublepole' double throw switch, to enable the direct "current or alternating current vsource to be selectively employed. The voltage of the source o f power may be suitably controlled, by adjusting the numberof cellsin the battery vvIl or controllingthe v'voltage ot the generator II. The

` circuit shownv includes further Lillustrative means for controlling the amount of currenttlowingin "the circuit, as the adjustable rheostat l5; and

suitable means'for determining the amount. of

'current flowing therein, as ,thecurrent meter or milliammeter IO. f

The output of the circuit Vl I, as shown, l

is` preferably' connected by means of a suitable switch I'Lto'be` applied to the currentelectrodes C1,y Cz, Figure 12, which may be located as in Figurel. i, M 1 V The resistivity or impedisivity .measuring circuit I 2, herein exernpliiiedebyv a potentiometer circuit, is adapted to be connected to the potential, electrodes P1P: of a grounddconilguration,

as, for example, the ground` conguration of '.Figure 1,'preferablyfbymeansoi aswitcliV I) of .V...,..Su1iab1e form'- is usualin lthe art oi geophysical surveying, reversing switches, (notshown) may be employed f for" interchanging'the connections to, C1Cz and yfor interchanging tlieconnections to .P1P`z, to ob- ".jtainV the properrelativepolarityor reverse the ection of measurement' of resistivity, as desind.

'I 'he measuring circuit' I2 comprises means for receiving the potential vderived from the potential ground electrodes, and ior;directly'frea`ding the ground resistivity determining the same, t In Y the preferred form, this direct reading means 1 comprises' a galvanometer or null current l'indicatorv 20," such as a sensitivega.l vanomete1 `,'l which may be provided with suitablemeans, such as a copper oxide rectlile, `for operating upon 'alter- `natinggcurrent; a calibrated potentiometer- 22| and by onployinotho doublepolo double-throw v switchr IIj-.to connect lthe resistance, Il alone in serieswith ythe input to measuring-circuit I 2., `in

'lieu of the'` potential eleotrodeo P1, Pi.

Now, referring to Equation .7, knowing thecurrent flowing `ifi.,circuiiffil y(by reading enammeter Ilthe cina-entl as adjusted by rheostatiI5) 'and knowingthe v value of resistance-Il", the ac-` 'tual vvoltage Eapplied to the input of, the meas- 10 uring circuit I2is'easi1y determined, Then with A the' current lI (indicated at I6)y adjusted in preanda vpotentiometer current source fcomprisinga' *potentiometer current controller, as the adjustable rheostat 22; and af source of, direct. or alternating current, herein thejv battery 23 or alter- ]nating currentinput leads 26. Where it is desited to faointateseleotivo use ofoitnor direct oralternating current, as abovementioned, a suitable switch',as` a double pole donblethrowy switch 25,1s arranged to connecteither typeof potentioineter current source (i. v.e` ,23v or 28). into the i. circuit. 'i

'rhov potenticnn'oterV genenmv intimated oy zu, inthe preferred fOrm, comprises a calibrated determined ratio' tothe distancey d between the electrodes Crand Cz of theconfiguration to be used,'and"rwith,a knowledge of the constant K of `auch .configurationnthe proper adjustment of means of rheostat the potentiometer vcurrent (by While this may appear `involved, the 4operation 4" is really quite simp1e, as showngfor example, by

thel procedure when using then c oniiguration described above under e caption Simpliedv species-0f method..".

` .With this conilguration,4 irom'Equationl-z,

`measuredunder this condition, the electrical re- "fsistivity wquldoqual isitimos 10o, oriamo'ohm ucalibrated resistances ZI', leach having, inieile'ct,

fa resistance equal tothat ofthe slide wire. The

contact switch 2| 1 thuspermits raising the volt- "age in'units 01.100, andthe slidewire 2|" subvdivides the 100 vu nitson it into single units. YThe galvanometer 2l indicates when the "applied and adjusted voltages [between switch ,2 Id I and 2 I b.

templated In simplest form this provision may y La 1111.11 readios'of salvanamajring circuitris "conditionedfoidirect readingof resistivity. Tnet is, ,tno -ir'istrument w111 now multiply anyr ground voltage vapplied to tit'byI 1.91,

fsentlfrneters.A yThe"potentiometer scale 2'I` of, the

measuring circuit, therein`)' re, j` With thisy ground configuration, should read notf 100 millivblts, `but 191 millivolts,'f

Nowgiwithswitchesn.and lnnthe; down po- 1 sition; (Figure 2) ancl rheostat JI.'i Vad iu'sted j. so

' that 'jammete'rf Ii'fshows a` current ofyl0 milli f amperes, and with""'a j'lOohni resistance ali-I8, it will be"aloiliilrentf thatlthdvgltag. applied through switch4 Il to ythe vinput ofthe potentiometencircnitf-lwomd noy 10o miuiv'oits. Tnosnoe' vwire potentiometer 2| is'now set, not for '100,1butA for-191i (as-by iofchldins'pne seotionijw and'91 units pf. 2 I, lbtwean the, 'inout members, ZI (and 2id) .'F yTheir ,by#adjusting rho tfzzitoi obtain ther measurand will givea vdirecifreading of382 of resistivity between 2Il and' 2Ib,.for a null onv 20 vbe made by employing astandard potentiometer current source', as a standard cell at 23,' for example. Under these conditions, the adjustment of the current in the potential current 'circuit 2I mustuse the relation' of Equation 7; with E as .A t

the 'standard-cell voltage.

f when 200 millivoltsfare' 'applied'fthroughfswitch I9; 951/2 lln'itS kr0f. resistivity' 50 `mi1liv01ts are thus applied, etc;

Tiieinstrument being thus adjusted switches f nj and la are' .throwntosurnoymg position, and

However, as 'geophysical surveying isfrequent- 1y conducted under extreme'weather c onditiona in vwhich a standard cell is aptto'lfail, theinvention contemplates as preferable, anfimpr'oved calibrating or scale adjustingmeans exemplified by'circuit I3, Figure 2;

This calibrating, conditioning, or scale adjustingcircuit, in the'form shown, consists of a high resis'tancel connected in series with a 16u/" re-v 'sistance 18e.' "lfhese resistancea for convenience Amay have values,'of say 1,000`ohmsand'10 ohms,y

respectively.

Suitable provision is madei'or connecting the currentcircuit II to the measuring circuit I2 `by in accordance with .the premise v:for Equation 5a,

the rheostat I5 is adjusted tor obtain a current reading on nr iilliarrimeter'v I6 corresponding to the ldistancef between electrodes Cr: and `C2 (i.`4 e.y 50 i milliainpejres l"for 5o feet) with this' applied current, the lmembers" 2 Id and -2 Ii are* adjusted /for'anull on galva'ometer `20, an'd they "readingv of thes potentiometeribetween these members "at v"such ybalanced conditi'c'iifiwill"bel the apparent earthresistivity.v Sometimesf'due to the/charway of these resistances I8, I8,I in the. form yshown in Figure 2, by employing the double-pole double-throw switch Il to connect the resistors i I8, I8'-L in `series with the outputof current cirlcuit I I,iny lieu ofthe current electrodes C1, C2;

.- -acter-of the' `grouni',.itmayfbeniore convenient to adjustthe'currenttcrfon `rnilnnmmetor Is) to 5 millianiperes instead ofj50- (or similarfratio for different Vdistances d) inw'hichcase thepoten- 4plied by 10.

g Generazieation y;l The same rgeneral principlesv areiemployedand the same generaLmethod is 4followed, .in ,ingl with alternatingf current;

operatsame potential drop across the said scale length, 'so as to produce a null in the input circuit-galvanometer. v For use with eitheralternating currentor direct current, the milliammeter il will be of the eter 20' may be either of the electrodynanometer type or a d'Arsenval type of galvanometer'provided with a suitable rectifier, as a copper oxide rectifier, for use with alternating current. l

' Now. if alternating current is to be applied to the ground, the alternating source will be applied across the (non-inductive) resistors It', ila as before, and the root mean square current, times the value of resistance Ila will constitute the indicated input voltage.

The potentiometer local alternating current will then be adjusted by rheostat `It and phase shifter 21 to bringthe instantaneous input and vponent (see my copendingapplieation Serial No.

333,752 nled May '1, 1940, for example).

While the method and means herein described are especiallyadapted for making measurements of the ground .constantswithout the laborious calculations which lusually accompany such observations,'it is understood that they may be used in the solution of "mathematical relations which have variable parameters similar to thoseudiscussed in the equations herein.

In addition the present invention enableafacile classiilcation of materials yof which the medium may consist, for example. in the of clay, the direct current resistivity'has a definite value,

and the alternating current impedisivity has a" relatively low Vcomplex or phase shift component at various frequencies. By c0ntrastin the vcase of quartz, whileahigh direct current resistivity is indicated, the alternating current impedisivity has a relatively higher complex 4or phase shift component. Thus, the method of this invention contemplates comparative readings ofimpedi- 'sivity under types of currents, as direct local voltages applied to the galvanometer 20 v into such'relation as to obtain a null.

Irrespective of whether the galvanometer 20 is of the electrodynanometer type, Aor of the dArsenval type provided `with a rectifier, the

ometerreading for balancey will directly indicate the apparent impedisivity amplitude vand kthe phase shifter the angle associated with this arnplitude. f a

It will be appreciated thatin the alternating current case, the impedisivity has the form of a complex operator which embodies both magnitude and time phase and in which the complex component owes its origin to the permeability and dielectric constant of the medium underobservation.

- This particular complex value musty vnot be confused with the complex valuedue tothe fact that the resistivity in the vmedium is directional, as mentioned in the above discussion of the configurationv of i ground electrodes. It should beborne in mind that va similar variation also exists for the dielectric property and permeability, so that the complex alternating component of impedisivity also v has a complex space component. For this reasonf-.wherenthe imaginary or transverse resistivity 4or'. imp edisivity is not to be considered, the measurements will preferably be made in a direct line between .C1 and C: (see for example, my prior Patent No. 1,951,760, granted March 20, 1934), and where the non# isotropic character of the medium is to be determined, the measurements will preferably be made at right angles through the mid-point of that line, to eliminate the effect of the real comcurrent, pulsatingcurrent, and alternating currents of di'erent' frequencies; land the apparatus, in its more comprehensive aspects', contemplata an instrumental combination capable of making measurements of 'more than one type.

In thisconnection the alternator lla, Fig. 2,

may be of thetype adjustable to supply more than one given frequency or kind of.'current. It Vwill further be seen that inasmuch as itis preferred, in practicing the present invention, to maintain a definite value of I/d (seeintrol duction to Equation 6), more uniform comparative results between different surveysmay be attained, as the variable factors introduced b ecause ground resistivity usually does not exactly follow Ohms law even for currents (see Patent No. 1,9 5l,'160)',7are'- minimized.

Reference is made to my copending application yentitled "Geophysical surveying, executed March 17, 1938, ser, No; 200,947, med April e. 193s, for

.supplemental and comparative' purposes.

From the foregoing description of vpreferxe embodiments of my invention it will be apparent that except where expressly usedonly with alternating currentthe term impedisivity is genericy to eitherldirect ,current resistivity or to the alternating current equivalent thereof,v and the term' is correspondingly employed in the following claims.

'I claim: l. A method roi! measuring electrical imf "pedis'ivity of a medium comprising kthe steps of v laying out a configuration ,for`applying,. from a source, electrical energy to the medium and for ypicllrlng up potentials existing in the energyeld thus created in the' medium, 'said configuration being one for which the relatlonishknown between the geometrical constants of the configuration, the electrical energy applied thereto, the potentials picked-up therefromand the unknown apparent impedisivity of thev medium;

`supplying velectrical energy to said configuration of a value in predetermined ratio to vthelsizeof said configuration; electrically proportioning the scale of a potential balancer to multiply potential indications by a factor rendering the Apotential balancer scale direct reading in magnitude of impedisivity for said known configuration with energy applied in accordance with said ratio and balancing picked up potentials-with the so adjusted potential balancer; whereby the 'apparent -impedisivities of the medium embraced by the 2,277,707 y n k from a source, electrlcalfenergyto a medium, i

coniiguration are: readable directly on the'potential balancerscale.

2. A method: according toclaim 1 in whichfa common alternating current source is employed for supplying electrical energy to the conguration and to proportionl the scale of the potential balancer; and in whichthe method further comprises the steps of changing theY relative phase of the currentfsupplied to the conflgurationand to the potential balancer to bring the alternating potentials applied to the balancer in cancelling phase, and measuring the phase changeintroduced to produce suchphasing as a direct measure of the phase change component ofl impedisivity of the medium' embraced bythe configuration.

3. A method of measuring electrical impedisivity of a medium comprising the steps of laying out a configuration of electrodes comprising current electrodes for applying, from a source, electrical energy to the medium, and potential electrodes for picking up potentials existing in the energy ileld thus created in the medium, said configuration of electrodes being one for which the relation is known between the spacings of the electrodes, the electrical energy applied to the current electrodes, the'potentials picked up at the potential electrodes, and the unknown apparent impedisivity of the medium; supplying electric current to said current electrodes in predetermined ratio to the electrode spacings; electrically proportioning the scale ofy a potential balancer to multiply potential indications by a factor rendering the potential balancer scale direct reading in magnitude of impedisivity of the medium for said known con- 1 figuration energized in accordance with said ratio; and measuring potentials picked up at said potential electrodes with the so adjusted potential balancer: whereby the magnitudes of the apparent impedisivities of the medium embraced by the configuration are directly indicated by the potential balancer scale.

4. A method of measuring alternating current impedisivity comprising the steps of: laying out a configuration for applying from a source an alternating current to a medium and for picking up potentials existing in the alternating current field in the medium; said configuration being one for which the relation is known between the geometrical constants of the configuration, the alternating current applied thereto, the potentials picked up therefrom, and the unknown apparent impedisivity of the medium; selecting a definite ratio for the value of current applied and the spacing of the points of current application in the configuration; proportioning the scale of a potential balancer to multiply alternatingA and for receiving vfor, n'ieasurementvv potentials .produced inthe resulting electrical field in the medium: 4in combination; a current circuit comprisingat least one source of current, a current adjustingjdevice', andja .current measuring d evice; a potential'bfalancing circuit comprising -a voltage divider, at least one. source fof, voltage therefor, means "for adjustingthe "voltage applied to said vvoltage divider to varythe voltage drop per scale unit thereof, andajpotential circuit includinga Igalvanomete'r and embracing means for including in circuit `therewith* a lvariable number of scaleffunits of said potential `divider; 'a calibrating circuit'connectable to.- derive a known potential from said current circuit and connectable'toapply said known potential to said potential'circuit to enable adjustment of the voltage drop Vof said potential divider to render the potential ,scale thereof fixedly related to impedisivity for a known geometric conflgui ration supplied with current from said current circuit in known ratio to the size of the configuration; means forconnecting said current cir- -cuit to the energy applying Aconnections of the configuration; and means for connecting said potential circuit tothe potential vreceiving connections of the configuration; substantially as and for the purpose described.

6. yA system according to claim 5 in-which said l source of current and said source of voltage are separate D. C. sources.

7. A system according to claim 5 in which said source of current and said source of voltage are a common A. C. source provided with a phase shifter to shift the relative phase of voltages applied to said voltage divider Vfor eliminating all current ow in said potential circuit.

8. A system according to claim 5 in which said source oi.' current and said source ofvoltage are a common source provided with means for eliminating all current ilow in said potential circuit.

9. In combination; a pair of current electrodes adapted to be electrically connected, in mutually spaced relation, with an earth volume; a pair of potential electrodes adapted to be electrically connected, in mutually spaced relation, with a portion of the earth volume within thezone ofy influence of said current electrodes; a calibratlng circuit (I3)l comprising a voltage drop resistor, current input terminals connected thereto, and potential output terminals connected to pick Y up at least a portion of the voltage drop across current potential indications by the proper factor to renderthe potentiometer scale thereof direct reading for the magnitude of impedisivity when the said definite ratio exists; supplying alternating current to said potential balancer from the same source from which current is applied to said medium; applying the potentials picked up from the configuration to various numbers of units of the potentiometer scale of the potential balancer and simultaneously adjusting the phase of the potentiometer current until balance of the potential balancer is attained; and reading the impedisivity magnitude and phase shift from the potentiometer and phase shifter, respectively, of the potential balancer.

5. In a system for measuring impedisivities, of the type employing a configuration for applying,

said resistor; a current circuit (Il) selectably connectable to the current electrodes and to the' current input terminals of said calibrating cir-v cuit, said current circuit comprising at least one source of current, a rheostat and an ammeter; a potentialbalancer circuit- (I2) comprising a variable resistance, at least one source of potential, and means for impressingcsaid source of potential across said variable. resistance to produce a voltage drop per unit of said resistance controllable by varying the said resistance, said potential balancer circuit further comprising a galvanometer circuit including means for embracing in circuit a continuously variable portion of said variable resistance; said galvanometer circuit being selectably connectable to said potential electrodes and to thev potential output terminals of `said calibrating' circuit; substantially as and for the purposes described.

10. A combination according to claim 9, in which a current supplied by said source of current and a potential suppliedby said source of potential are identically alternating in character, and in which the combinationiurther comprises means for shifting the relative phase o! said current and said potential; whereby said source of potential and the Calibrating and potentialelectrode potentials selectably connectable to' said galvanometer circuit may be rela-y tential electrodes and calibrated to read directly in terms of impedisivity of the earth volume between said potential lelectrodes vfor a predetermined arrangement of electrodes and a predetermined ratio between ythe current of said current circuit and the spacing of said current electrodes. and said current circuit comprising indicator means for facilitating adjustment of said current-adjusting means to l produce the said predetermined ratio, substantially and as for the purposes described.

12. A combination. according to fclaim 11, in which means supplying alternating current energy identical in character energize said current circuit and voltage divider, and in which the combination further comprises means forvshifting the relative phase of said energizations.

FREDERICK W. LEE. 

